Systems and methods for detecting and controlling bed height in fluidized bed reactors

1. A system for detecting and/or controlling the level of solids in a fluidized bed reactor, the system comprising:

a fluidized bed reactor having a top end, a spaced-apart bottom end, a height, an outer surface, an inner surface, an interior space, and further comprising:

a reaction zone comprising a cylindrical portion extending from the bottom end toward the top end and having a reaction zone circumference, and

an expansion zone above the reaction zone and having an expansion zone circumference at each vertical distance along the expansion zone that is greater than the reaction zone circumference;

a plurality of nuclear radiation sources disposed along the outer surface of the fluidized bed reactor between the top end and the bottom end, each at a different vertical distances from the bottom end; and

a detector array comprising a plurality of radiation detectors disposed along the outer surface of the fluidized bed reactor between the top end and the bottom end, each at a different vertical distance from the bottom end,

wherein a line between each radiation detector and each nuclear radiation source passes through the interior space of the fluidized bed reactor, and

wherein the plurality of nuclear radiation sources includes at least one radiation source having a radioactivity of 5000 mCi located on the outer surface of the reaction zone, the expansion zone, or both.

2. The system of claim 1 , wherein each of the plurality of nuclear radiation sources is located within a first vertical plane that contains the vertical axis of the fluidized bed reactor, and each of the plurality of nuclear radiation detectors is located within a second vertical plane that contains the vertical axis of the fluidized bed reactor.

3. The system of claim 2 , wherein the angle between the first vertical plane and the second vertical plane is about 0°, such that the plurality of nuclear radiation sources and the plurality of radiation detectors are disposed on opposite sides of the fluidized bed reactor.

4. The system of claim 1 , wherein the detector array further comprises a computer configured to compare the measured intensity of the nuclear radiation at the plurality of radiation detectors, and determine the level of solids in the fluidized bed reactor.

5. The system of claim 4 , wherein the computer is further configured to adjust the level of solids in the fluidized bed reactor by adjusting one or more of a solids removal rate, a fluidization velocity, a catalyst feed rate, a reactor gas density, a reactor gas composition, a reactor temperature, and/or a reactor pressure.

6. The system of claim 1 , wherein the fluidized bed reactor further comprises a distribution grid at the spaced-apart bottom end.

7. The system of claim 1 , wherein the expansion zone comprises a conical transition portion between the reaction zone and the top end of the fluidized bed reactor, such that the diameter of the transition zone increases with increasing distance from the reaction zone.

8. The system of claim 1 , wherein the plurality of nuclear radiation sources includes at least 3 nuclear radiation sources.

9. The system of claim 1 , wherein the plurality of radiation detectors includes at least 4 nuclear radiation detectors.

10. The system of claim 1 , wherein the plurality of nuclear radiation sources includes 4 nuclear radiation sources and the plurality of radiation detectors includes 6 nuclear radiation detectors.

11. The system of claim 1 , wherein one or more of the plurality of radiation detectors is an ionization chamber, a proportional counter, a Geiger-Müller tube, or a scintillator.

12. The system of claim 1 , wherein one or more of the plurality of nuclear radiation sources is a Cesium gamma (γ) radiation source, a Cobalt gamma (γ) radiation source, or any combination thereof.

13. The system of claim 1 , wherein the plurality of nuclear radiation sources includes at least one 5000 mCi radiation source, at least one 2000 mCi radiation source, at least one 1000 mCi radiation source, and at least one 500 mCi radiation source.

14. The system of claim 1 , wherein the fluidized bed reactor is a polyethylene reactor.

15. A system for detecting and/or controlling the level of solids in a fluidized bed reactor, the system comprising:

a fluidized bed reactor having a top end, a spaced-apart bottom end, a height, an outer surface, an inner surface, and an interior space;

a plurality of nuclear radiation sources disposed along the outer surface of the fluidized bed reactor between the top end and the bottom end, each at a different vertical distances from the bottom end; and

a detector array comprising a plurality of radiation detectors disposed along the outer surface of the fluidized bed reactor between the top end and the bottom end, each at a different vertical distance from the bottom end,

wherein a line between each radiation detector and each nuclear radiation source passes through the interior space of the fluidized bed reactor, and

wherein the plurality of nuclear radiation sources includes at least one radiation source having a radioactivity of 5000 mCi.

16. The system of claim 15 , wherein the wherein the plurality of nuclear radiation sources further includes at least one 2000 mCi radiation source, at least one 1000 mCi radiation source, and at least one 500 mCi radiation source.

17. The system of claim 15 , wherein each of the plurality of nuclear radiation sources is located within a first vertical plane that contains the vertical axis of the fluidized bed reactor, and each of the plurality of nuclear radiation detectors is located within a second vertical plane that contains the vertical axis of the fluidized bed reactor.

18. The system of claim 17 , wherein the angle between the first vertical plane and the second vertical plane is about 0°, such that the plurality of nuclear radiation sources and the plurality of radiation detectors are disposed on opposite sides of the fluidized bed reactor.

19. The system of claim 15 , wherein the fluidized bed reactor is a polyethylene reactor.